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Simplifying (9x + -4)(5x + 6) + (9x + -4)(3x + 4) = 0 Reorder the terms: (-4 + 9x)(5x + 6) + (9x + -4)(3x + 4) = 0 Reorder the terms: (-4 + 9x)(6 + 5x) + (9x + -4)(3x + 4) = 0 Multiply (-4 + 9x) * (6 + 5x) (-4(6 + 5x) + 9x * (6 + 5x)) + (9x + -4)(3x + 4) = 0 ((6 * -4 + 5x * -4) + 9x * (6 + 5x)) + (9x + -4)(3x + 4) = 0 ((-24 + -20x) + 9x * (6 + 5x)) + (9x + -4)(3x + 4) = 0 (-24 + -20x + (6 * 9x + 5x * 9x)) + (9x + -4)(3x + 4) = 0 (-24 + -20x + (54x + 45x2)) + (9x + -4)(3x + 4) = 0 Combine like terms: -20x + 54x = 34x (-24 + 34x + 45x2) + (9x + -4)(3x + 4) = 0 Reorder the terms: -24 + 34x + 45x2 + (-4 + 9x)(3x + 4) = 0 Reorder the terms: -24 + 34x + 45x2 + (-4 + 9x)(4 + 3x) = 0 Multiply (-4 + 9x) * (4 + 3x) -24 + 34x + 45x2 + (-4(4 + 3x) + 9x * (4 + 3x)) = 0 -24 + 34x + 45x2 + ((4 * -4 + 3x * -4) + 9x * (4 + 3x)) = 0 -24 + 34x + 45x2 + ((-16 + -12x) + 9x * (4 + 3x)) = 0 -24 + 34x + 45x2 + (-16 + -12x + (4 * 9x + 3x * 9x)) = 0 -24 + 34x + 45x2 + (-16 + -12x + (36x + 27x2)) = 0 Combine like terms: -12x + 36x = 24x -24 + 34x + 45x2 + (-16 + 24x + 27x2) = 0 Reorder the terms: -24 + -16 + 34x + 24x + 45x2 + 27x2 = 0 Combine like terms: -24 + -16 = -40 -40 + 34x + 24x + 45x2 + 27x2 = 0 Combine like terms: 34x + 24x = 58x -40 + 58x + 45x2 + 27x2 = 0 Combine like terms: 45x2 + 27x2 = 72x2 -40 + 58x + 72x2 = 0 Solving -40 + 58x + 72x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 29x + 36x2) = 0 Factor a trinomial. 2((-5 + -4x)(4 + -9x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25Subproblem 2
Set the factor '(4 + -9x)' equal to zero and attempt to solve: Simplifying 4 + -9x = 0 Solving 4 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -9x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9x = 0 + -4 -9x = 0 + -4 Combine like terms: 0 + -4 = -4 -9x = -4 Divide each side by '-9'. x = 0.4444444444 Simplifying x = 0.4444444444Solution
x = {-1.25, 0.4444444444}
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